# Analytical solution to a constrained quadratic programming

I am looking for an analytical solution of the following quadratic programming problem : $$\min_x x^TA x, s.t. 1^T.x = 1, 0 \le x \le 1$$

where A is positive definite.

I am not looking for a QP solver, I am aware of their existence and their performance. I am looking for an analytical solution, or a theorem proving that there is none.

Is anybody aware of any solution? Or a starting point?

Thank you very much in advance

• Did you try KKT? – Rodrigo de Azevedo Nov 16 '19 at 10:03
• yes, but not successfully. The solution is well known without the inequality constraints and is easy to find... – mtiret Nov 17 '19 at 11:09
• It would enrich your question if you posted all of the work you have done so far. This question has been asked before, unsurprisingly. – Rodrigo de Azevedo Nov 17 '19 at 11:16
• – Rodrigo de Azevedo Nov 17 '19 at 11:22
• – Rodrigo de Azevedo Nov 17 '19 at 11:26